{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:VDZJ3JS7FMEXBDP4UDDTGZXS6N","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8eab0519f8d431d3827db0660a3030972a8b5927c717f4f624a147038cb909d6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AT","submitted_at":"2025-09-14T19:02:30Z","title_canon_sha256":"b2f476a9d717815711d81849b3eb11524820ff5fdd00f2e7a50f5fd69449e1d6"},"schema_version":"1.0","source":{"id":"2509.11393","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.11393","created_at":"2026-06-25T01:17:45Z"},{"alias_kind":"arxiv_version","alias_value":"2509.11393v2","created_at":"2026-06-25T01:17:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.11393","created_at":"2026-06-25T01:17:45Z"},{"alias_kind":"pith_short_12","alias_value":"VDZJ3JS7FMEX","created_at":"2026-06-25T01:17:45Z"},{"alias_kind":"pith_short_16","alias_value":"VDZJ3JS7FMEXBDP4","created_at":"2026-06-25T01:17:45Z"},{"alias_kind":"pith_short_8","alias_value":"VDZJ3JS7","created_at":"2026-06-25T01:17:45Z"}],"graph_snapshots":[{"event_id":"sha256:e84c63f7825c3235e9ca4c6748d2c84220f5f3aa7764aa712da1a2e67f28767d","target":"graph","created_at":"2026-06-25T01:17:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2509.11393/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This work develops a comprehensive algebraic model for rational stable parametrized homotopy theory over arbitrary base spaces. Building on the simplicial analogue of the foundational framework of May-Sigurdsson for parametrized spectra, and the homotopy theory of complete differential graded Lie algebras, we construct an explicit sequence of Quillen equivalences that translate the homotopy theory of rational spectra of retractive simplicial sets into the purely algebraic framework of complete differential graded modules over the completed universal enveloping algebra $\\widehat{UL}$ of a Lie m","authors_text":"Alejandro Saiz, Aniceto Murillo, Yves F\\'elix","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AT","submitted_at":"2025-09-14T19:02:30Z","title":"A new approach to rational stable parametrized homotopy theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.11393","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:84b417f2e61dd952400c856f68a29a57b29fbbc1c679985695eec12fb1b8ad3b","target":"record","created_at":"2026-06-25T01:17:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8eab0519f8d431d3827db0660a3030972a8b5927c717f4f624a147038cb909d6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AT","submitted_at":"2025-09-14T19:02:30Z","title_canon_sha256":"b2f476a9d717815711d81849b3eb11524820ff5fdd00f2e7a50f5fd69449e1d6"},"schema_version":"1.0","source":{"id":"2509.11393","kind":"arxiv","version":2}},"canonical_sha256":"a8f29da65f2b09708dfca0c73366f2f34b982eba17f88f51644c8683f64a8614","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8f29da65f2b09708dfca0c73366f2f34b982eba17f88f51644c8683f64a8614","first_computed_at":"2026-06-25T01:17:45.984801Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-25T01:17:45.984801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pKyiJUF0fK7i7kOHV4m/w3zbL8lnKj0kuvH9+BV8QKoOW6KOs5V0aa3iujTyU03bib4P3DK27vpi88iWDtZoCw==","signature_status":"signed_v1","signed_at":"2026-06-25T01:17:45.985203Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.11393","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:84b417f2e61dd952400c856f68a29a57b29fbbc1c679985695eec12fb1b8ad3b","sha256:e84c63f7825c3235e9ca4c6748d2c84220f5f3aa7764aa712da1a2e67f28767d"],"state_sha256":"911f26e6d3ec4aa6ecc20aae10a8a4cce2be0aa62d307d7a2158eaffb8cd4be6"}